For a first-order reaction,if $75\%$ of the reaction is completed in $15 \ min$,then the time required for $90\%$ completion of the reaction will be ........... $min$.

The rate equation for a first-$order$ reaction is given by $R = R_0 e^{-kt}$. $A$ straight line with positive slope is obtained by plotting which of the following? ($R_0 =$ Initial concentration of the reactant,$R =$ concentration of the reactant at time $t$)

For the first-order gaseous reaction $A_{(g)} \to 2B_{(g)} + C_{(g)}$,the expression for the rate constant $K$ in terms of initial pressure $P_0$ and total pressure $P_t$ at time $t$ is:

$A$ radioactive substance decomposes such that after $100 \ min$,its concentration becomes $1/8$ of the original concentration. Calculate the rate constant $(k)$ and half-life time $(t_{1/2})$.

Consider a certain reaction $A \rightarrow \text{Products}$ with $k = 2.0 \times 10^{-2} \ s^{-1}$. Calculate the concentration of $A$ remaining after $100 \ s$ if the initial concentration of $A$ is $1.0 \ mol \ L^{-1}$.

For the $1^{st}$ order reaction,the half-life is $5 \ minutes$ when $[A] = 0.1 \ M$. If the concentration of $[A]$ becomes twice,then the half-life becomes: